Two-dimensional (2-D) autoregressive moving average (ARMA) models are commonly applied to describe real-world image data, usually assuming Gaussian or symmetric noise. However, real-world data often present non-Gaussian signals, with asymmetrical distributions and strictly positive values. In particular, SAR images are known to be well characterized by the Rayleigh distribution. In this context, the ARMA model tailored for 2-D Rayleigh-distributed data is introduced -- the 2-D RARMA model. The 2-D RARMA model is derived and conditional likelihood inferences are discussed. The proposed model was submitted to extensive Monte Carlo simulations to evaluate the performance of the conditional maximum likelihood estimators. Moreover, in the context of SAR image processing, two comprehensive numerical experiments were performed comparing anomaly detection and image modeling results of the proposed model with traditional 2-D ARMA models and competing methods in the literature.

中文翻译：

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用于 SAR 图像建模的二维瑞利自回归移动平均模型

二维 (2-D) 自回归移动平均 (ARMA) 模型通常用于描述真实世界的图像数据，通常假设为高斯或对称噪声。然而，现实世界的数据通常呈现非高斯信号，具有不对称分布和严格的正值。特别是，众所周知，SAR 图像具有良好的瑞利分布特征。在此背景下，介绍了为二维瑞利分布数据量身定制的 ARMA 模型——二维 RARMA 模型。导出了 2-D RARMA 模型并讨论了条件似然推断。将所提出的模型提交给广泛的蒙特卡罗模拟，以评估条件最大似然估计器的性能。此外，在 SAR 图像处理的背景下，